Fiat is flawed, sure. But the way things are right now, Bitcoin is a gamble, not some magic fix.
So, pick your poison.
There are fundamental differences between fiat and bitcoin though.
Fiat is designed to lose its value over time. So, if you save in Fiat, then that's a pretty bad idea. You need to invest in any kind of asset with that fiat.
On the other hand, bitcoin is designed to increase in value over time, so you don't have to invest into something else. Although some countries consider bitcoin an asset, so that means ymthat you are saving in an investment instrument.
It makes a lot of sense to save in bitcoin, as long as you have a medium to long term in mind (5-10 years minimum )